I=S

There's a lot of people wandering around the internet who are very confused about Investment = Saving. Maybe they have been mistaught, or maybe they have mislearned? I don't know. But I'm doing this as a public service, even though it's a thoroughly boring job for me. Someone's got to do it. And since I've done it almost every year for the last 33 years, it might as well be me. "Ours the task eternal" is Carleton's motto.

Let's get the arithmetic out of the way first, then I'm going to simplify, back up, and explain what it all means.

Start with the standard national income accounting identity:

1. Y = C + I + G + X - M

On the left hand side of we've got sales of (Canadian) newly-produced final goods (and services) Y. On the right hand side we've got purchases of (Canadian) newly-produced final goods (and services), divided up into various categories. Consumption, Investment, Government expenditure, eXports, and iMports.

2. S = Y - T - C

This is a definition of Saving as income from the sale of newly-produced goods minus Taxes (net of transfers, which are like negative taxes because the government gives you money instead of taking it away) minus Consumption.

Substitute equation 1 into 2 to eliminate Y and you get:

3. S = C + I + G + X - M - T - C

You can eliminate C in 3, and rearrange terms to get:

4. I - S + G - T + X - M = 0

If you simplify, by assuming a closed economy with no exports or imports, you get:

5. I - S = T - G

If you simplify further, by assuming no government spending or taxes, you get:

6. I = S

(Or, if you like, you could define S as "national saving" to include both private saving plus government saving, which is defined as T-G.)

Now let's talk about what it means.

Equation 1 is an accounting identity. It is just like saying "the number of apples sold = the number of apples bought". You can't sell an apple without somebody else buying it. That's what the words "buy" and "sell" mean. If we add up all the apples sold, and add up all the apples bought, we should get exactly the same answer. If we didn't, it means we miscounted, or had a different definition of "apple" in the two counts, or did the two counts over different time periods, or made some other screw-up. And National Income Accounting is the art of checking all the possible screw-ups we might make, and trying to make them as small as possible, so we can get as accurate a picture as possible of economic data.

For example, if you are counting apples sold by the Canadians who produced them, and counting apples bought by Canadians, you have to remember that some Canadian apples get sold to foreigners, and some apples bought by Canadians weren't produced in Canada. That's why you have to add exports and subtract imports in equation 1 to make it add up right.

Since apples sold = apples bought, and bananas sold = bananas bought, then apples and bananas sold = apples and bananas bought. If it adds up for each good, it also has to add up across all the goods. So it really doesn't matter if we add up the physical number of apples and bananas, or add up the market values of apples and bananas, or add up the market values adjusted for inflation, or what. A+B=A+B. A+2B=A+2B. 24A+32B=24A+32B. Whatever. Equation 1 is true in nominal terms, without any inflation adjustment. Equation 1 is true in real terms, adjusted for inflation. Equation 1 is even true if we adjust for inflation in some totally daft manner, just as long as we are consistent in our daftness on both sides of the equation. Of course, we get a different number for Y depending on which we choose, and some of those numbers will be more useful than others, but we should (unless we screw up) get the exact same number on both sides.

(There are lots more potential screw-ups we could make: like how exactly we define and count "Canadian" "newly-produced" "final" goods. But go read any intro economics textbook if you are interested, because it's not the main topic of this post.)

Now, I have defined Y as goods sold. Normally, we think of Y as "income", or "production". And you can think of cases where these don't seem to be the same.

For example, suppose you produce 100 apples and you don't sell them? If we want Y to measure the production of apples, and not just sales of apples, we have to remember to include apples that the grower consumes himself, or adds to his inventory of apples. "He sold them to himself, either for Consumption or for inventory Investment". That's a fudge, of course, but it's a fudge we need to make if we want Y to mean "production" as well as "sales".

Here's a second example. Suppose you have 100 apples in inventory, that were produced last year, and the price of apples suddenly goes up $1. You have just made a capital gain of $100. Shouldn't that capital gain be included in your income? Well perhaps it should, or perhaps it shouldn't. But if you want Y to mean "income", you had better not include it. Y has to be restricted to mean "income from newly-produced goods".

All the above was accounting. It wasn't really economics at all. "Apples sold = apples bought" is always true. But it tells us nothing whatsoever about what determines the number of apples traded. It is totally silent on what causes the number of apples bought-and-sold to increase or decrease. Or why it is bigger in some countries than in others. Is it the weather? Is it people's preferences for apples? Is it government rationing? Is it the rotation of the planets? There are 1,001 different theories of what determines the quantity of apples traded, and all of those theories are consistent with the accounting identity of apples sold = apples bought. Because "apples sold" and "apples bought" are just two different ways of describing the exact same number.

One of those 1,001 theories is the simple economic theory taught in Intro Economics. Supply and demand. Quantity demanded is the quantity of apples people would like to buy, given the price of apples, their income, etc.. Quantity supplied is the quantity of apples people would like to sell, given the price of apples, their productive abilities, etc.. The demand curve shows how quantity demanded varies with price, holding other things like income etc. constant. The supply curve shows how quantity supplied varies with price, holding other things like productive capacity etc. constant. And, according to this theory, the price of apples adjusts to make quantity demanded equal to quantity supplied, where the demand and supply curves cross. At that equilibrium price, and only at that equilibrium price, all 3 quantities are equal. Quantity demanded = quantity bought-and-sold = quantity supplied. According to this theory it is the supply and demand curves that determine quantity bought-and-sold.

That theory could be wrong. That's one of the dangers of having a theory that actually attempts to explain what causes or determines the facts. It could be wrong. But if we want to explain the world, that's the risk we have to take. One can easily think of examples where this theory would be wrong. For example, if the government imposes a binding price floor on apples it will be wrong. In that case, Intro Economics would replace it with a slightly modified theory: the quantity of apples traded is determined by the demand curve and the price the government sets; the supply curve plays no role. With the price fixed above where supply and demand curves cross, quantity demanded = quantity bought-and-sold < quantity supplied. In that "semi-equilibrium" actual purchases will be equal to and determined by the quantity of apples people want to buy (demand) at the fixed price. But the actual quantity sold will not be equal to nor determined by the quantity people want to sell (supply).

And if the government instead sets a binding price ceiling on apples the original supply and demand theory will also be wrong, but in a different way. In this case, according to the Intro Economics textbook, it's the supply curve and price that determine quantity bought-and-sold. In "semi-equilibrium", quantity demanded > quantity bought-and-sold = quantity supplied. Actual purchases will be equal to and determined by the the quantity people want to sell (supply) at the fixed price.

(The key assumption in all three of the above theories is that trade is voluntary. You can't force people to buy more than they want to buy; and you can't force people to sell more than they want to sell. So quantity actually bought-and-sold will equal whichver is less: quantity demanded; or quantity supplied. Only in full equilibrium, at exactly the right price, are all three quantities equal. Otherwise we are in what i call "semi-equilibrium", where only two of the three quantities are equal, and the third is bigger than the other two.)

"Apples sold = apples bought" is an accounting identity that is always true, but tells us nothing about what determines that quantity.

"Apples demanded = apples supplied" is an equilibrium condition. It might not be true. It is part of a theory that does try to explain what determines the quantity of apples bought-and-sold. That theory might be true, or might be false. But it is a theory about the world, and the risk of being false is an unavoidable occupational hazard of trying to explain the world.

Now, that was microeconomic theory. Let's switch back to macroeconomic theory. What's that got to do with I=S?

Look back at equation 1, and assume a closed economy with no government. You get Y = C + I. That equation is exactly the same as I = S. The two are mathematically equivalent. Just different ways of saying the same thing. But Y = C + I is a lot easier to compare to the microeconomic equilibrium condition "supply = demand". So I'm going to do that first, then come back to I = S.

For an economy that produced only apples, "Y = C + I" tells us that apples sold equals apples bought (some for consumption, some to be added to stocks as an inventory investment). But that accounting identity tells us absolutely nothing about what determines the quantity of newly-produced goods bought-and-sold. It does not explain why it changes over time, or is higher in some countries than in others. There are 1,001 different theories, all compatible with that accounting identity, that do try to explain what determines Y.

Here is just one of those 1,001 theories. This theory will be found in most Intro Economics textbooks. It's the simple "Keynesian Cross" theory. This theory is very similar to the microeconomic theory above of a market for apples with a binding price floor, where quantity supplied exceeds quantity demanded. This theory says that the quantity of goods bought-and-sold will be equal to and determined by the quantity demanded, and will be less than the quantity supplied. But there's a clever macro twist. The macro twist is that the quantity of goods demanded depends on income, and income is equal to the quantity of goods bought-and sold.

This theory can be described by three equations:

7. Y = Cd + Id

Cd means "desired consumption". It's the quantity of consumption goods people would like to buy, given their income etc. Some economists call Cd "ex ante consumption". But a simpler name would be "quantity of consumption goods demanded", just like in micro. And Id is just the same, except it's "desired investment", or the quantity of investment goods demanded. And equation 7 is a "semi-equilibrium condition". It says that actual quantity of goods bought-and-sold (Y) will equal quantity of goods demanded (Cd+Id).

8. Cd = a + bY (where a>0 and 0<b<1)

9. Id = Ibar

Equations 8 and 9 are the behavioural equations. They tell us what determine desired consumption and desired investment. Desired consumption is an increasing function of actual income, and desired investment is fixed at some exogenous number, called Ibar. (That's supposed to be a bar over the I, but I can't write it).

Substitute 8 and 9 into the equilibrium condition 7, to get:

10. Y = a + bY + Ibar

Solving for Y we get:

11. Y = [1/(1-b)][a+Ibar]

Now that's a theory of the world. It might be false. But if true, it explains what determines the quantity of goods bought-and-sold. It says Y is determined by desired investment (and by the parameters a and b in the consumption demand function).

And it is a simple matter of math to relate that back to I=S. Simply define "desired saving" Sd as:

12. Sd = Y - Cd

So "desired saving" means "that part of income that people do not desire to spend on (newly-produced) consumption goods". What do they want to do with it instead? It could be anything, except spend on (newly-produced) consumption goods. They might want to spend it on newly-produced investment goods, they might want to buy government bonds, or corporate bonds or shares, or buy antique furniture, or add to their stocks of currency under the mattress. You name it, and if it's something you can want to do with your income (after taxes), other than spend it on newly-produced consumption goods, it's "desired saving".

We can re-write the old semi-equilibrium condition 7 as:

13. Y - Cd = Id

And substitute the definition for Sd into the left hand side to get:

14. Sd = Id

We can read 14 as "desired saving equals desired investment". Or "ex ante saving equals ex ante investment". It is mathematically equivalent to the semi-equilibrium condition 7. It's just another way of saying "quantity of goods bought-and-sold equals quantity of goods demanded". Only now it gets rearranged to become "quantity of goods bought-and-sold minus quantity of consumption goods demanded equals quantity of investment goods demanded". Which is a bit of a mouthful.

Substitute 8 into 12 to derive the desired saving function from the desired consumption function:

15. Sd = -a + (1-b)Y

Desired saving is an increasing function of income.

Substitute the desired investment and desired savings functions 9 and 15 into the "semi-equilibrium condition" 14 to get:

16. -a + (1-b)Y = Ibar

Rearrange 15 to get

17. Y = [1/(1-b)][a+Ibar]

Which, you will notice, is exactly the same as 11. You get exactly the same results whether you start from Y=Cd+Id or Id=Sd. And of course you should, They are exactly the same semi-equilibrium condition, just re-written.

But if you start with the same semi-equilibrium condition and add different behavioural functions you will get a very different theory of the world. For example another macroeconomist would say that desired investment and desired saving also depend on the rate of interest, and that the central bank will adjust the interest rate so that desired saving equals desired investment at potential output. In which case you cannot say that desired investment determines desired saving (or vice versa) because they are both endogenous variables, and it is the central bank that determines the equilibrium level of income. And yet another macroeconomist would say that that's not quite right either, because if the central bank tries to set the interest rate too high or too low the result will be accelerating deflation or inflation, so in the long run, if it doesn't want to destroy the monetary system, the central bank can only set it at some "natural rate" where desired saving equals desired investment at the level of income determined by the long-run supply of output.

In other words, the semi-equilibrium condition Sd=Id leaves open the question of what variable(s) adjust (or is adjusted) to bring the two sides into equality. It might be Y, as the Keynesian Cross model assumes. But it might be the rate of interest. Or the price level. Or anything else.

Let me sum up the main lessons.

First, you can't get anywhere with just accounting identities, if you want to explain the world. Convert that accounting identity into an equilibrium condition, and add some assumptions about people's behaviour, and what adjusts to what, and you might have a theory.

Second. The I=S approach is exactly equivalent to the Y=C+I approach. The latter is more easily re-interpreted as the semi-equilibrium condition Y=Cd+Id, which is the macroeconomic version of "apples bought-and-sold = quantity of apples demanded", but Id=Sd is saying the exactly the same thing. (I was taught both these methods of representing the old Keynesian Cross model back in high school).

Third. The key question is not just the equilibrium condition you assume, but what variable or variables you assume adjust to make that equilibrium condition hold. What are the behavioural functions? Different behavioural functions will give you a very different theory.

Fourth. A lot of economists wasted an awful lot of time and ink getting this stuff straight 50 years ago. If you start your theory with I=S as an accounting identity, it really is your responsibility to try to explain to anyone reading the difference between I=S as an accounting identity, and Id=Sd as some sort of equilibrium condition, and why that difference matters. Because, as I said at the beginning, there's an awful lot of poor lost souls wandering around the internet who have just discovered the marvellous truth of I=S as an accounting identity, and think they have found some magical philosopher's stone that "mainstream" economists have never heard about, and that this blinding flash of divine truth will lead them to the Promised Land. It's a bit like being accosted at airport terminals by people with a glow in their eyes repeating "apples sold equals apples bought". Because that's exactly what they are saying.

Comments

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There is no equilibrium in the real world. It would have been better and more realistic if you just dropped your equilibrium assumption together with Sd=Id and just stayed in the real world. Because this is where the *real* difficulty of S=I is.

“First, you can't get anywhere with just accounting identities, if you want to explain the world.”

I assume all this is mostly the result of your frustration with MMT.

The inverse to your statement is:

“You can’t explain the world without conforming to accounting identities”.

If you examine a lot of the MMT thinking about economics, you’ll find that this latter idea is highly operative. Scott Fullwiler has some powerful ways of expressing this in some of his papers, but I’m too lazy to look them up right now.

In the most simple form, your accounting identity is S = I.

If you attempt to explain the world according to your economics as a change from time period 1 to time period 2, you must have:

S (1) = I (1)

And

S (2) = I (2)

This is the case no matter what the absolute temporal positioning of period 1 and period 2 are. Both can be in the past, one in the past and one in the future, or both in the future.

What this means is that accounting is a constraint on economics.

And that’s something you guys (you to be defined relative to attitude to MMT) are very loathe to accept.

Sergei: do you want to do away with I=S altogether, even as an accounting identity? Are you saying it's false? OK, if that's what you mean, I will leave you and JKH to have a fun argument (I will join JKH). Or are you saying that it's not useful? I might have some sympathy with that.

If you think that demand and supply are both irrelevant in determining the quantity of apples actually bought and sold, that's an interesting position. Not one I agree with, but interesting.

JKH: If I find a theory in which quantity of apples sold is not equal to quantity of apples bought, I am very happy to agree that's not a very good theory. I'm not at all loathe to accept that. That goes whether we are talking about this year, last year, next year, or whatever year, century, month, week, etc. Or whether we are talking about apples, bonds, antique furniture, whatever, or even money.

JKH,
"What this means is that accounting is a constraint on economics"

You obviously missed the point of Nick's post. Saying that apples bought equals apples sold doesn’t tell you anything meaningful about the market for apples. Saying that S=I in every period doesn’t tell you anything meaningful about the macroeconomy. All old-Keysian, New Keysian, Monetarist, Austrian, RBC and neoclassical growth theory models are all consistent with S=I. S=I is not a constraint on any of these theories.

I can't think of any economic model that doesn't impose the accounting identities. The whole point of Nick's post is to point out that they are *routinely* incorporated into the development of the model en passant.

Are you thinking of some economic theory in which accounting identities are violated? Which one?

Gregor and Stephen: I was thinking on the same lines. I think I did *once* referee one paper that maybe (if my memory is correct) violated an accounting identity. (The model was over-determined). Just in case you need to ask, I recommended rejection.

Good refresher post. The "return to basics" S=I, made popular recently by certain individuals, could be akin to a "brilliant" physicist coming into a room and intuitively looking at a problem, surrounded by much complicated maths, empirical assumptions and the like, and stating the elegant solution on a single chalkboard, not necessarily with any equations beyond the basic one. It does happen (I've seen it) so I wouldn't discount it.

Krugman claims his freshman economics class teachings are explaining the current economic environment rather well.

1. What is your recommended path for the US govt budget balance over the next, say, 10 years? (in % of GDP terms would be most clear)
2. What is your assumption regarding the US current account balance?
3. Give answers to 1 and 2, what will S-I be?
4. Is your answer to 3 desirable or even sustainable?

BTW, using CBO assumptions for 1 and 2 during the late 1990s and 2000s and then answering 3 and 4 for ourselves made it clear that CBOs projections (and most everyone else's) were dead on arrival. If the accounting identities were so obvious and trivial, why can't CBO figure them out?

As JKH says, any relevant theory has to conform to accounting identities (and if one thinks that's all there is to MMT, then that's just silly, but I'll leave that one for now). "apples sold= apples bought" just demonstrates the point hasn't been properly understood.

The CBO example is more along the lines of what we're talking about--or asking the Republicans in the US Congress to answer those 4 questions, for instance, particularly the ones against raising the debt ceiling. If you can find 1 neoclassical economist who teaches his/her students to answer my 4 questions above when teaching macroeconomic policy analysis, I'll be more than moderately surprised. (Not to mention the fact that any neoclassical economist using DSGE models with a transversality condition can't answer #4 anyway, as Charles Goodhart has pointed out over and over.)

No, I think the better challenge is to find an economic theory that doesn't respect the accounting identities. My claim is that they all do. Saying that "any relevant theory has to conform to accounting identities" is telling us something we already know.

My suggestion was not that economic theory must conform to accounting identities, but that economic analysis must conform to it, including all forecasting and risk analysis. That is a stronger statement than the same for formal economic theory alone, which hopefully has been vetted for accounting integrity. So I think Scott's question is a good example of what the issue is.

Scott: "BTW, using CBO assumptions for 1 and 2 during the late 1990s and 2000s and then answering 3 and 4 for ourselves made it clear that CBOs projections (and most everyone else's) were dead on arrival."

But most models I can think of wouldn't make any *assumptions* about 2, given an assumption about 1. You make an assumption about the government budget balance (and maybe monetary policy), then let the model answer 2 and 3. I could maybe imagine someone like Pat Buchanan making an assumption about both 1 and 2. Because he's planning to impose import quotas or something. Otherwise 2 and 3 are both endogenous variables (though the sum of 2 plus 3 is exogenous, of course, given 1).

"...(and if one thinks that's all there is to MMT, then that's just silly, but I'll leave that one for now)."

I have come across too many *followers* of MMT who I can only interpret as believing that everything in MMT follows as a matter of logic from accounting identities. That's *one* of the things that triggered this post (though I also wrote it because a lot of people, not just MMT *followers*, find I=S confusing). I can't think that the *leaders*, like yourself, believe this. And I know one can't be held responsible for everything one's followers believe. But something weird is going on here. It happens far too often to be just a fluke. My guess is that a lot more will listen to you setting them straight on this than will listen to me.

"(Not to mention the fact that any neoclassical economist using DSGE models with a transversality condition can't answer #4 anyway, as Charles Goodhart has pointed out over and over.)"

I haven't done any macro in ages and can barely remember the IS-LM model. But, if i understand everything said in the post correctly when we plot the usual S and I curves in {S_I, r} space these are effective supply and demand curves for loanable funds for a given level of income. And if they intersect at a rate of interest that is negative so that the ZRLB holds then it must be that Income must fall given our equlibrium conditions that jointly determine Y and r.

Hi Nick, why did the mainstream models not see the GFC coming, while heterodox economists, including MTM economists did? Did you foresee it? Can you explain it in terms of your model? How about doing a post on that.

Regarding the endogeneity, yes, obviously all three are endogenous in their own ways. The point is, then, for instance, why hasn't the economics profession ever (to my knowledge) queried CBO on its assumptions for S-I when it makes its projections? Why doesn't Laurence Kotlikoff tell us what he expects the effects on S-I to be if we follow his advice and permanently cut deficits by 6% or whatever his latest projection of the fiscal imbalance is?

My suspicion is that your model above isn't what economists think about when they think of S-I. What shows up in all of the textbooks once it's time to do analysis is I = S + T-G + M-X, the so-called national saving identity. Most analyses of this identity incorrectly assume that there is some pool of saving, and we easily go from here to the inapplicable loanable funds market and financial "crowding out" by govt (in terms of how "loanable funds" are actually generated in the aggregate, but not that there aren't supply and demand in individual markets like, say, for venture capital; that's another story, though).

Regarding Goodhart, see this as a quick overview: http://www.voxeu.org/index.php?q=node/4283

Thinking more about what Scott said about some forecasts violating accounting identities, this is my guess about what happened. Instead of using *one* consistent model to make the forecast for *everything*, the problem is broken up into bits. One group forecasts X, with one model, another group forecasts Y, with a different model, and a third group forecasts Z, with a third model. And it would only be by sheer fluke if X,Y, and Z are in any way consistent with each other. Even if they were (by fluke) accounting consistent, it would be very unlikely if all 3 were consistent with any reasonable economic theory.

And Scott is, of course, quite right to complain about such internally inconsistent forecasts.

Is it possible to construct a prototypical example of how people are abusing accounting identities? I would have thought something in the way of an iconic error might be sticking in your mind as to exactly how people are going terribly wrong on this.

I’ve also noticed you touch on the nature of supply and demand curves a number of times. It seems to me as simple as acknowledging that both are functions of an independent variable that itself covers a fairly wide domain of possibilities. The eventual, operative value of the functional value (i.e. quantity sold or bought) reflects just one of those independent variable possibilities, depending on the interface between supply and demand functions as well as other possible influences (e.g. government intervention, etc.) I’m I wrong on this myself? How are people not understanding this?

Finally, is it possible that some of your concern is related to the outright MMT rejection of the loanable funds theory? (I wrote this before seeing Scott’s latest.) That is fundamental to MMT, and I would have thought that it rejects a great deal of related theory that you might otherwise expect to substantiate the extrapolation of accounting identities associated with economic outcomes. People are not bringing theories that you are comfortable with to the accounting party because they are not comfortable with the theories that you comfortable with.

I think you are missing an important viewpoint on I=S by not translating it back to the real world: In order to invest the national savings we need a financial system. That system is absent from the equation, because we always assumed it would function efficiently, moving the money from the place where it is saved to the place it is needed for investment. With a financial system that doesn't function you will never get I=S. The problem we need to solve is thus: how do we get investments going without depending on the banking system?

The only ones that can invest the money without help are the ones saving the money, thus the government should stimulate that. The only other solution is taxation and have the government reinvest.

But more generally (I don't know who Laurence Kotlikoff is and what his theory is) not all models give the same salience to the same variables. It might be a bit like a traditional monetarist asking a New Keynesian what his forecast implied about the stock of money and velocity? The New Keynesian would just shrug his shoulders and reply "M and V will take care of themselves".

On your second paragraph: When I first learned the Keynesian Cross, we were taught it two ways. The first was the standard Y=AE and AE=C+I+G+X-M way (with the two lines on the board). The second was the Withdrawals = inJections way. Same Y on the horizontal, then two curves: W=S+T+M, and J=I+G+X. Equilibrium Y determined where the two curves cross.

The two ways of showing the same theory are of course equivalent. The second has fallen out of favour. I think it's because "S" is such a "non-thing", and hard to interpret intuitively. The first has a much easier "output = output demanded" interpretation.

But, of course, both ways have really fallen out of favour past intro economics. It's only old guys like me who understand what you are talking about (or part of it, anyway). Does Y adjust to equilibrate S=I? Or does r adjust to equilibrate S=I? (And some MMT *followers* don't think anything has to adjust to equilibrate S=I, because they must be equal).

JKH: "Is it possible to construct a prototypical example of how people are abusing accounting identities? I would have thought something in the way of an iconic error might be sticking in your mind as to exactly how people are going terribly wrong on this."

Scott Sumner's blog seems to be overloaded, but it was some of the comments there that were the trigger. But let me make something up, to give you an illustration:

"It makes no sense to ask what variable adjusts to equilibrate S and I. S and I are always necessarily equal, so anybody (like Nick Rowe) who asks this question just doesn't understand basic accounting."

Yep, something like that did rather stick in my mind. It is terribly wrong. A good old-fashioned extreme Keynesian would also say that's terribly wrong (and would answer "Y adjusts to equilibrate desired S and desired I, and that is precisely how Y gets determined").

And saying the above is a terrible mistake is in no way related to the loanable funds theory per se. The loanable funds theory (at its crudest) says r adjusts to equilibrate S and I. Keynesian economics (at its crudest) says "no that's wrong, it is Y that adjusts to equilibrate S and I; r adjusts to equilibrate Md and Ms". Two very different theories (and one can imagine many more non-loanable funds theories of what adjusts to equilibrate S and I) but all are in conflict with the mistaken view that S and I don't need equilibrating, because they are always equal.

(Funnily enough, in the olden days we used to associate the view that S is necessarily the same as I with Say's Law, and the denial of the logical possibility of general gluts, which is about the most extreme opposite to MMT one can think of!)

Your 7:19 sounds good to me. If you don't know who Kotlikoff is, then you're way ahead, IMO!

Regarding this: "It makes no sense to ask what variable adjusts to equilibrate S and I. S and I are always necessarily equal, so anybody (like Nick Rowe) who asks this question just doesn't understand basic accounting."

I agree with you . . . that's not correct at all. A lot of MMT supporters misinterpret or at the very least don't have a very precise understanding of the sector balances (as we call s-i = g-t +x-m) as we explain and use them in analysis. Sort of like when I see someone write "the national debt is equal to private savings" or something like that--ouch.

Regarding this: "It might be a bit like a traditional monetarist asking a New Keynesian what his forecast implied about the stock of money and velocity? The New Keynesian would just shrug his shoulders and reply "M and V will take care of themselves"."

I see where you're going there--there has to be a reason why paying attention to the pvt sector balance is important to us, which obviously comes from our Minskyan approach. And it's obviously not as important to others--Goodhart's interpretation of DSGE models suggests that the latter ignore solvency issues for the pvt sector altogether. Further, it goes to a fundamental difference b/n fiscal and monetary policies--the latter can only "work" to end a recession if the pvt sector releverages, whereas with the former the pvt sector can deleverage and still sustain or perhaps even increase spending. We think that difference is important, but it doesn't show up hardly anywhere in most discussions of the differences. (Clearly some of the reason for this is that fiscal policy is viewed as requiring releveraging for the pvt sector, too, in the neoclassical view, via adherence to the intertemporal budget constraint and potential Ricardian equivalence effects.)

"Further, it goes to a fundamental difference b/n fiscal and monetary policies--the latter can only "work" to end a recession if the pvt sector releverages, whereas with the former the pvt sector can deleverage and still sustain or perhaps even increase spending."

I'm going to put words into your mouth here a bit, but bear with me.

One of the problems with S-I=G-T (ignore foreigners) is the level of aggregation. Even if G-T=0 the private sector can still deleverage. If the debtors increased their saving, and the creditors decreased theirs, leaving aggregate desired saving the same, private sector (gross) debt would decrease, and I would want to describe that as "deleveraging".

You would I think agree. And this does not in any way contradict your model. But, to make the same point you made earlier, some ways of presenting the accounting identities do (in some weird way) lead our eyes to look towards certain things and ignore others.

"It makes no sense to ask what variable adjusts to equilibrate S and I. S and I are always necessarily equal, so anybody (like Nick Rowe) who asks this question just doesn't understand basic accounting."

The thing is, the accounting identity has to hold even out of equilibrium, so unless you believe in continuous equilibrium, it's misleading to talk about equilibrating S and I. Something happens, out of equilibrium, that determines S and I in the very short run, and then something else happens that brings the model to equilibrium (possibly changing S and I in the process and possibly not).

In the simple Keynesian cross model (closed economy, no government, no inventories), the thing that happens initially out of equilibrium is that firms decide how much to invest. Their desired investment is then realized as actual investment, and, in the very short run, it determines saving, because everyone who receives income from that investment immediately saves it. (If you make the very short run short enough, that has to be the case, because they don't have time to spend it.) And when the equilibration happens, it has no effect on these values of S and I. The equilibration happens through acts of matched saving and dis-saving without ever altering the level of investment. I would argue, therefore, that in the Keynesian cross model, nothing adjusts to equilibrate S and I; rather I immediately determines S, and then C and Y adjust to equilibrate each other.

I'm less clear on what happens out of equilibrium in the loanable funds model. Does it only work with continuous equilibrium? Otherwise, what happens in the very short run if, for example, people suddenly decide to save more? I'm thinking the immediate effect is to reduce, simultaneously, both income and interest rates without affecting investment. Then the equilibration happens when firms respond to the lower interest rates by investing more, thus bringing income and saving back up (and also causing interest rates to rise to some intermediate level, possibly feeding back on saving in a cobweb etc.). But again it's misleading to say that r adjusts to equilibrate S and I. In my example, r changes before the equilibration, and then I adjusts (along with further changes in r) to equilibrate Y.

If I am a debtor and I pay down my debt to you instead of spending, I have reduced my spending out of income and deleveraged.

But you have not received any income from this aside from debt service (interest), just a portfolio shift from a loan or bond to deposits. You would have to make an additional assumption that the creditor now spends more out of income (i.e., as a result of the portfolio shift now moves to spend instead of save), which I don't see any inherent reason for; the creditor could desire to continue saving and just convert to a time deposit or whatever (the creditor could surely spend, but I don't see the behavioral reason to spend BECAUSE the debt has been paid down).

Further, if it is a bank that is the creditor, the payment to reduce debt has simply resulted in a debited deposit of the payor and a debited loan for the bank. There is clearly no reason for the bank to "spend" more out of income.

Now to turn to traditional Keynesian macro . ..

In the aggregate, S-I will depend on a number of factors (interest rates, etc.) that will determine how or even if the reduced spending of one affects aggregate desired spending out of aggregate income (i.e., desired "net saving"). Yes, some others may spend more out of income as a result--perhaps the debtor's reduced spending reduces someone else's income, but that person doesn't reduce spending but reduces saving. In other words, we certainly can get the same result as you do, but not necessarily via the creditor's actions (and I would argue probably not because of the creditor's actions). Or, interest rates could fall and others could as a result spend more out of income and again keep aggregate S-I from rising.

But if the desire to deleverage is widespread enough, then it reduces incomes and shows up as reduced spending on imports and/or reduced tax revenues in the aggregate, and S-I rises.

(Furthermore, it's important to add that "deleveraging" could simply be reducing debt ratios or debt service ratios, so simply borrowing less or stop borrowing, rather than actually paying debt down. In that case, again, we aren't talking about creditor behavior but the aggregate picture.)

So, what we have is the debtor spending less out of income and very possibly the creditor spending the same out of unchanged income.

In the end, I don't necessarily agree with your overall point (we can have some deleveraging but keep S-I from changing, and the aggregation is complex and important to understand), but I don't don't think the creditor's desire to spend/save is really the place to look either in the micro or macro case. I think this is one of the problems/flaws folks like Krugman have in not completely understanding what is meant by a balance sheet recession relative to a liquidity trap.

I agree with you given the assumptions made (no govt, no foreign sector, etc.).

I was interpreting the statement differently, but it's late and I've forgotten how (not real late, but I'm tired, so I'm using that as my excuse). When I first read Nick's response to that quote above, I saw his point immediately, though, or so I thought--perhaps Nick can help me out (and I hope I agree with whatever Nick writes or I'll feel really stupid--won't be the first time, though, or last.)

"monetary policies...can only "work" to end a recession if the pvt sector releverages"

Nick:

"If the debtors increased their saving, and the creditors decreased theirs, leaving aggregate desired saving the same, private sector (gross) debt would decrease, and I would want to describe that as 'deleveraging'"

That could happen, but it does not seem to constitute monetary policy "working" to end a recession. At least it's not the mechanism by which monetary policy would work.

However, I think what Scott is missing is that some other monetary policy mechanism that has the effect of ending the recession by other means could also result in deleveraging. In an open economy, currency depreciation would be an example. Indeed, currency depreciation operates very much like fiscal policy, except that the fiscal stimulus comes from exports and from import replacement rather than from the government.

Another example, or rather a class of examples, would be the effect of monetary policy on asset values. Even if no new borrowing happens, lower interest rates raise the value of long-lived assets, such as equity and houses, because interest-bearing assets become less attractive, making other assets more attractive in comparison. This has several effects. For one thing, it produces immediate deleveraging by raising the asset side of balance sheets without raising the liability side. It also has a wealth effect that induces people to spend more. And finally, by raising the value of investment goods relative to the cost of producing them, it makes it more advantageous to demand such goods.

Finally, I would note that monetary policy can operate by affecting expectations. If the central bank can convince people that it can and will raise the price level, there will be incentives to start raising prices and output immediately, and this will result in deleveraging by transferring wealth from creditors to debtors. This does require a certain Tinkerbell effect, but I believe a sufficiently aggressive central bank could apply a fairly effective whip to Tinkerbell's back.

this post is all about flow consistency. i can't think of any models off the top of my head that are flow inconsistent. MMT is referring to something different. it's referring to the consistency between flows, stocks AND stocks. there are plenty of models that aren't stock-flow consistent (the most glaring example being cbo forecasts).

"This has several effects. For one thing, it produces immediate deleveraging by raising the asset side of balance sheets without raising the liability side. It also has a wealth effect that induces people to spend more. And finally, by raising the value of investment goods relative to the cost of producing them, it makes it more advantageous to demand such goods."

It's extremely difficult to price the value of a firm when earnings from year 20 to year 100 are 80% of the firm's value. Really you are just throwing a lot of dust in the eyes of investors, creating bubbles which will be followed crashes. Odds are more likely that the resulting prices are the wrong ones, and economic growth will suffer as a result.

Finally attempts to increase the value of in-place assets disproportionately favor the wealthy -- as the starting concentration of assets is not uniform.

There are much better and simpler ways to stimulate demand and clear debts that don't rely on throwing a wrench into the valuation process.

The Nikkei didn't do very well since ZIRP, although it had a lot of volatility and in the short run ZIRP seemed to succeed in raising asset prices. Land didn't do that well, either.

You get a similar "slow multiplier" if you assume production responds slowly, and that any change in investment is initially met out of inventories, but in that case it's desired saving that determines actual investment in the very short run. A change in desired investment causes no immediate change in actual investment, because there's undesired inventory rundown.

Another different way to get a slow multiplier is to assume no inventories, but production responds slowly. A sudden increase in desired investment causes a line-up of frustrated buyers. Only later does output respond to restore the semi-equilibrium condition.

In the simplest loanable funds model, an increase in desired saving causes the rate of interest to fall, with no change in Y. If I is slow to respond to r, then r must fall by a larger amount, sufficient to completely offset the increase in desired S.

(My personal views on all this S=I Keynesian Cross vs loanable funds stuff are quite different again, but I've kept quiet about them in this post, because it would just be a distraction, since my views are too unorthodox. As you perhaps know, I don't believe in the Paradox of Thrift, but I do believe in the paradox of hoarding. It is an excess demand for the medium of exchange, not an excess of desired saving over desired investment, that causes Y to fall. An excess demand for antique furniture is an excess of saving over investment, but it cannot cause a recession.)

Scott and Andy: the normal way of dividing the economy up is into: households; firms; government; and foreigners. That's roughly in line with Y=C+I+G+(X-M). But that's not the only way to divide up the economy. For questions of debt and deleveraging, I find it more useful to divide it up into creditors and debtors. Sure, that way of dividing up the economy doesn't tell us anything by itself. We need to add some behavioural conditions. A fall in interest rates will cause borrowers to want to borrow more, but will also cause lenders to want to lend less. Y will presumably increase, but what is the net effect on the quantity of borrowing and lending, when we remember the accounting identity that borrowing=lending? It's not obvious. It will depend on the differences between the two groups' elasticities of borrowing and lending with respect to interest rates and income. (I confess I haven't actually worked out the math.)

But someone who says that lower interest rates will increase borrowing and therefore debt (which you hear a lot), has forgotten the other side of the accounting identity. Borrowing = lending. And lower interest rates reduce desired lending.

"But someone who says that lower interest rates will increase borrowing and therefore debt (which you hear a lot), has forgotten the other side of the accounting identity. "

OK -- if we assume that the government controls nominal borrowing rates, then the "demand to lend" falls out of the picture for purposes of clearing the lending markets. Banks can always create money and lend it out, irrespective of what individuals want.

In that case, the lack of a desire to lend shows up as inflation -- it really means households don't want to hold onto the deposits created by banks as a result of lending. It doesn't mean that borrowers do not get funded, or that the lending does not occur.

Nick: do you want to do away with I=S altogether, even as an accounting identity?

No, surely I do not. But what makes this identity interesting is a dynamic process and not the static statement of S=I. Accounting world world lives in accounting periods but there are a lot of things happening within each and every period to render your Sd=Id completely useless if not misguiding.

The accounting identity S=I is an ex-post identity. That is why Sd=Id is meaningless outside of equilibrium. It is meaningless to this world which is never in the equilibrium. Therefore imposing Sd=Id on the real world is misguiding. Yet many theoretical and political conclusions are driven from such misguided understanding.

Nick wrote "One of the problems with S-I=G-T (ignore foreigners) is the level of aggregation. Even if G-T=0 the private sector can still deleverage. If the debtors increased their saving, and the creditors decreased theirs, leaving aggregate desired saving the same, private sector (gross) debt would decrease, and I would want to describe that as "deleveraging"."

I don't follow this at all. Mmt sees S' as vertical money or S-I. Please say it is S' you are referring to as savings?

Deleveraging relates to a reduction in horizontal money, not shifting vertical money from private creditors to private debtors which has no effect on gross savings(S'). Yes vertical money can be use to pay off a creditor of horizontal money, but the vertical money ends up with the horizontal creditor in order for there to be 'deleveraging'.

Scott wrote:" Sort of like when I see someone write "the national debt is equal to private savings" or something like that--ouch."

I hear Mmters say this all the time and assume they've not included cash, reserves or the word net ( as in net non-u.s. Government savings - ss surplus......) In Nick's case he'd take out investment as he includes it in his savings (S). Though I don't think he did above. It's tough communicating clearly.

If economists had gotten this stuff straightened out 50 years ago, we would not be having this lovely discussion, but alas and alack. (And, it has been lovely. Thanks to all.)

I would like to do away with I = S, as an accounting identity. Contra Sergei, I find Sd = Id comparatively harmless; a necessity, prehaps of derivation.

The double-entry bookkeeping of the National Accounts is based on the idea that every observable transaction gives rise to at least one pair of entries. So, when some product is sold, that product is also bought; the sale can be recorded and the purchase can be recorded. If the statistician has access to a record of sale, she's fully justified in inferring a purchase; in this way, somewhat spotty observation and records can be reconciled into a coherent picture of the whole. Two problems with "saving": first, in its common-sense meaning saving does not necessarily involve a transaction; saving is not-spending, which is not a transaction. Of course, some forms of "saving" do involve a transaction; transactional saving is also lending. So, if the national accounts were consistent, they could define saving = lending, and that would be true as a matter of accounting identity in a straightforward way. (And, actually, that's what they do, mostly.)

It seems to me that both the understanding of the national accounts and economic theory get twisted out of shape by this silly business of S = I. If the economist wants to posit an equilibrium in analysis, I'm fine with that, but the national accounts do not describe a system in equilibrium, so why should S = I? (I understand why; I'm arguing that the national accounts would be clearer, if this were not the convention. And, it is a convention, not an accounting identity, strictly speaking; since transactional saving/lending has no necessary, definitional relation to investment in inventories and capital equipment; it is just a matter of conventional presentation to make it so, to make Y equal to final product and estimate S with a big fudge.) The system described by the National Accounts is out of equilibrium; describe it as out of equilibrium. You may need equilibrium for derivation; you don't need equilibrium to make the books balance.

Winslow, I'm afraid I'm not conversant with "horizontal" and "vertical". Could you point to a succinct explanation?

I don't think leverage/de-leverage means much outside a context of financial intermediation. It is not a single interest rate matching a market of would-be creditors with would-be debtors; it is a yield curve, along which intermediaries attempt, through arbitrage (the carry trade), maturity transformation and portfolio diversification, to manage risk. Money as a medium of exchange gives way to money as a store of value, and medium of insurance and calculation.

IF you think in terms of financial intermediaries as the primary manufacturers of private debt, it is easier to imagine how debt can expand and contract, and carry effective aggregate demand with it. Also, central bank policy becomes less a matter of a single policy rate, than about managing inversions of the yield curve to induce recession.

Bruce,
I don't understand your 03.27AM post. You are right that Savings is an ambiguous term (and unfortunately the national accounting identity don't destinguish clearly between the household sector and the corporate sector which doesn't help in understanding). But the national accounts show a flow of money used to buy goods and services - and (in a closed economy without government for simplicity) income that is not spent on consumption goods and services (and that is how consumption is distinguished from investment) must both increase asset balances (i.e. savings net of depreciation) AND come from purchases of investment goods (since received income implies a transaction). There is no equilibrium involved with this - it is simply following firms and households income and expenditure. The key here is the somewhat arbitrary division of goods and services into final consumption and intermediate and capital goods. (Intermediate goods are of course mostly netted out).

Sectoral balances are flow measures. Private sector net savings (S - I) are just the money added into circulation by government deficit spending and an export surplus.

The money stock - as in total credit/debt on bank balance sheets - can go up and down due to private sector or government borrowing or repayment.

Sometimes a few people conflate private sector deleveraging with private sector net savings. This is obviously wrong. The better way to think about it is that total credit/debt will shrink with private sector deleveraging unless the government leverages up through increased deficit spending.

Maintaining a growing stock of money is important to maintain the flow of money in a growing economy. If the stock of money falls due to deleveraging, then the flow of money must also drop - reducing incomes (Y) and therefore affecting things like consumption (C), savings (S), taxes (T) or imports (M). But it's not that paying down debt directly reduces I without reducing S. Any discrepancy between I and S only arises due to government deficit spending or the trade balance.

I agree that savings can be ambiguous. You hear people saying that we must increase savings to boost investment - when the truth is that loans create deposits. You also hear people talking about how the chinese are great savers - saving 50% of their income - when this is just the export surplus and government deficits adding to 50% of Y.

"Sometimes a few people conflate private sector deleveraging with private sector net savings. This is obviously wrong. The better way to think about it is that total credit/debt will shrink with private sector deleveraging unless the government leverages up through increased deficit spending."

Yeah, I argued with Bill Mitchell about this. He insisted that deleveraging requires saving at the private sector level (not just saving by non-financial entities).

...there's an awful lot of poor lost souls wandering around the internet who have just discovered the marvellous truth of I=S as an accounting identity, and think they have found some magical philosopher's stone...

I suspect this is because the definitions of S and I are not quite intuitive to non-economists (and even to some economists, perhaps).

Imagine I earn $100 and put $10 in the bank, but the bank hasn't yet found a business to lend it to, so it hasn't been "invested". An intuitive way to describe this is: S=10, I=0 - oh look, S=I is violated!

Of course S is not really 10, because my saving is cancelled out by the bank's borrowing (or the bank's shareholders' borrowing if you like). That's without even getting into the question of whether the $100 is actually income.

People who think in the above way (which is not unreasonable given the normal use of English language) are inevitably going to be surprised by the assertion that S=I. This will lead to one of two responses: "don't be ridiculous, your economic theories of 'equilibrium' and 'rationality' are obviously wrong" or "wow, look at this amazing fact I discovered. Isn't the world a strange place? I will now show off my new cleverness to my unenlightened friends/fellow bulletin board readers."

If they were taught the technical meanings of S and I, or even that there are technical meanings, their amazement and confusion would quickly dissipate. Admittedly it would probably be replaced with boredom; good luck getting most of those people to read and understand this post. Thanks though - it's a good refresher, especially for those (like me) not formally trained in economics. I'm sure I have made similar mistakes in the past.

rsj: money does (generally) change things. But I'm not sure financial intermediaries do. This would be one of those cases where I would start out slowly. Start with barter, get the "bonds bought = bonds sold" accounting identity and equilibrium conditions right, then bring in money and/or financial intermediaries one at a time.

Sergei: "The accounting identity S=I is an ex-post identity. That is why Sd=Id is meaningless outside of equilibrium. It is meaningless to this world which is never in the equilibrium."

Dunno. If you were right, that would mean all of keynesian economics (plus all of classical and MMT and pretty well anything else that comes to mind) would be wrong. What would you replace it with?

Winslow: "I don't follow this at all. Mmt sees S' as vertical money or S-I. Please say it is S' you are referring to as savings?"

And you expect *me* to follow what you are saying there? You are speaking some very strange language. "Vertical money"?? "S'"???

Look, Scott understood what I was saying. Suppose I have a debt to you of $100. Suppose I drop my consumption by $100, pay you the $100, and you increase your consumption by $100. Then private gross debt has fallen, private consumption and saving have stayed the same in aggregate, and nothing changed with I,G,T,X, or M. If your accounting identities are stopping you understanding that, then you are being mislead by your own accounting identities.

"Deleveraging relates to a reduction in horizontal money, not shifting vertical money from private creditors to private debtors which has no effect on gross savings(S'). Yes vertical money can be use to pay off a creditor of horizontal money, but the vertical money ends up with the horizontal creditor in order for there to be 'deleveraging'."

What?????

"In Nick's case he'd take out investment as he includes it in his savings (S). Though I don't think he did above."

I have been using the absolutely standard economics definition of saving thoughout. S is defined as Y-T-C.

Bruce: "If economists had gotten this stuff straightened out 50 years ago, we would not be having this lovely discussion, but alas and alack."

Well,...*some* of us got it straightened out, but others haven't learned it. My post was an attempt to educate those latter people.

There is absolutely nothing new in my post, BTW. Any competent teacher of ECON1000 could have written something similar. (But I am sort of proud of the way I presented it, especially in relating Sd=Id back to "quantity demanded = quantity bougt-and-sold". I don't think many could have done that as clearly and accurately as I did, if you will excuse me blowing my own horn a little!)

I can't decide whether I agree or disagree with the rest of your comment. When we actually build macro models, we normally simplify massively, so the accounting becomes trivial. And it gets built into the agents' budget constraints. The problem starts when we try to relate variables in our models back to the data, which use NIA definitions of variables, which are necessarily based on a much more complicated world. Do the variables in our model mean the same things as the NIA data?

My surface impression is that you and Scott are talking a bit past each other at one level - you're sticking to the (S = I) "global" model, and he's venturing into the (S - I) sector model. Maybe I'm wrong on that.

BT: "Private sector net savings (S - I) are just the money added into circulation by government deficit spending and an export surplus."

That is really wrong, unless you are using "money" in a very strange way. Suppose the government sells a national park to a household, and uses the proceeds to buy newly-produced tanks. Ignore foreigners. G-T has gone up. S-I has gone up too. But there need be no change in the stock of money in circulation. National parks are not money, by any definition. Or the government could have financed the tanks by selling bonds. Indeed typically only a very small part of government spending is financed by the creation of base money. In Canada it is roughly $2 billion per year. Roughly 0.2% of GDP. And it has stayed at roughly that sort of level despite big swings in the government budget deficit or surplus of around 10% of GDP.

Look, this is a case where I do insist on people getting the accounting right.

Leigh: "I suspect this is because the definitions of S and I are not quite intuitive to non-economists (and even to some economists, perhaps)."

Agreed. I is not so bad. It's S that's the killer. Sometimes I think we should just drop S altogether, and instead talk about the demand and supply of: output, bonds, money, etc. It's money that is the genuinely weird one, precisely because it doesn't have a market of its own. An excess demand for apples shows up in the market for apples. An excess demand for bonds shows up in the market for bonds, etc., until we get to money. An excess demand for money shows up in all the markets for everything else, because all those other goods are bought and sold for money.

In which market can one buy savings? The purchase of capital is a capital transaction that leaves savings unaffected. Same for the purchase of bonds. The only way to save is to refrain from purchasing consumption.

"My surface impression is that you and Scott are talking a bit past each other at one level - you're sticking to the (S = I) "global" model, and he's venturing into the (S - I) sector model. Maybe I'm wrong on that."

What's the difference between "global" and "sector"?

The simplest case to illustrate my point about deleveraging is where G=T=I=X=M=0, so it's a model where the only good is a consumption good, and all loans are consumption loans between households. And desired saving must be zero in equilibrium. One person can pay off his loan to another household. If the first chooses to save and the second chooses to dissave, total desired saving stays the same at zero.

"Andy is right.

In Nick's model, S = I at all times, equilibrium or not.

Andy understands accounting."

Actual S = Actual I at all times, by definition. In my first model, explicating Andy's point, with the lag in the consumption function, it is also true that desired saving will equal desired investment at all times, because that model is always in *short-run* equilibrium. But that equilibrium will be moving over time, because of the "slow multiplier", so it takes time to get to the "long-run" equilibrium (actually an infinite time, since convergence is asymptotic).

In the other variants of the model, where it takes time to adjust production, it is true that actual S = actual I at all times (obviously), but *desired* S does not equal *desired* I at all times, because it takes time for Y to adjust to make them equal.

"The reason for the continuous operation of the identity is the inventory process, of course."

Not strictly. Imagine a haircut economy, so no inventories. (And no investment, for simplicity). Start in equilibrium with Sd=S=0. Then all of a sudden people want to consume more haircuts. But it takes time to hire more people to cut hair. The result is a line-up at the hairdressers. Actual S=0, but desired S is less than zero. People want to get a haircut, but can't. Quantity demanded exceeds quantity bought-and-sold.

Hey! Sure Andy understands accounting, but don't I understand it too (at least, for the purposes of S=I, because I know I don't understand a lot of what real accountants do)?

And your haircut argument applies to the service sector as a subset of the entire economy, where the service sector is particularly defined (artificially) to have net zero I. But the inventory argument still applies to the rest of it.

Good question. Answer: in the market for newly-produced investment goods; in the bond market; in the land market; in the market for antique furniture; etc.,.....and, most importantly *in no market at all*, by not spending part of the flow of money you have received as income, and keeping it in your pocket.

"The purchase of capital is a capital transaction that leaves savings unaffected. Same for the purchase of bonds."

Woah! If I decide to spend a *flow* of my income on a *flow* of purchases of machines or bonds, instead of spending it on a flow of consumption, then I have increased my saving. If I reduce my *flow* demand for bonds, and increase my *flow* demand for machines by the same amount, my saving is unchanged. If I sell a *stock* of bonds and use the proceeds to buy a *stock* of machines, my saving is also unchanged.

"Woah! If I decide to spend a *flow* of my income on a *flow* of purchases of machines or bonds, instead of spending it on a flow of consumption, then I have increased my saving."

No. But this to me is where your medium of exchange focus comes in very handy. Saving is what is not consumed - which typically shows up directly as medium of exchange used to settle income payments, but not used to settle consumption payments. Leaving the money in the bank is the primary example. From there, one can exchange what has been saved for other assets - anything but consumption of newly produced goods and services. But the act of saving is in what is not consumed - not in what the medium of exchange is subsequently used for instead (if anything).

JKH: "There's no I in a haircut economy, so your point is moot with respect to macro I = S, (although a fair one apart from that, at the micro level)"

I=S also holds equally true in a world with no investment. Since both I and Id by assumption are both zero, the S=I identity and Sd=Id equilibrium condition, simply become S=0 and Sd=0. My point is not moot at all. S=I also has to work in a haircut economy.

But if you like, imagine that investment too is a service, and you can't hold inventories of the newly-produced investment good. The farmer invests by hiring a firm to clear scrub from his land. If the scrub-clearing firm cannot increase production quickly, in response to an increased investment demand by farmers, we get desired investment exceeding actual investment, even in a world with no inventories.

We really ought to be able to tell the S=I story just as well in a world of fresh strawberries, services, and no inventories. Really, inventories are just a complicating fudge factor that prevents us seeing what's going on clearly. What slows down the adjustment to the keynesian multiplier equilibrium is not inventories, it's the slowness of hiring new workers and ramping up production in response to an increase in demand. That's way more important than the accursed inventories.

Thank you. :) You have answered a question I posed elsewhere last year:

If I = S, why does the term (I - S) appear in the identity,

(I - S) + (G - T) + (X - M) = 0 ?

The reply I got was more or less gobbledygook.

OTOH, if I had gotten the right answer, that to get I = S we assume that G = T and X = M, I might have thrown up my hands in disgust. As a layman, a major problem I have with public economic discourse is the unspoken assumptions.

Thanks Min! Another person for whom my post cleared something up. And nothing to do with MMT in this case.

There's another way to get S=I, in a closed economy. That's to re-define "S" as "National saving = private + government saving", where government saving is government "income" T minus government consumption spending Gc. You also have to include government investment spending in I. It gets trickier to stretch the meanings of S and I in an open economy though.

"If the scrub-clearing firm cannot increase production quickly, in response to an increased investment demand by farmers, we get desired investment exceeding actual investment, even in a world with no inventories."

Everything in that model is production of a service, and income is paid for that service as it is produced.

There is no inventory issue because there is no capitalization of the value of the service - because the value of the service is entirely accounted for by income, on a pay as you go basis.

If there is no capitalization, there is no investment, and no saving.

Yes, the multiplier gets slowed because production of the service is slower than desired. But that's beside the point about I = S.

JKH: the way I look at it is this: we have a flow of money coming into our pockets, *part* of which is income; and a flow of money going out of our pockets, *part* of which is consumption. Saving is the difference between those two *parts* of the flows in and out. The flow increase in the stock of money is the difference between the *total* flows in and out.

JKH: "If there is no capitalization, there is no investment, and no saving."

I don't understand "capitalization". But there certainly is capital and investment in my model. The stock of cleared land is capital (OK, land+capital, if you like). The flow of cleared land (acres cleared per month) is investment.

"You're starting to re-define stuff that just gets further and further away from real world application and intersection."

Whaat? My father cleared 50 acres of scrub from farmland in his life. It was one of his major investments. The whole of Canadian farmland fits my model. (OK, add field drainage in there too, along with scrub clearing.) That's a really big part of Canada's capital stock. This is much more real world than widgets! You urban fellow you!

No. You're redefining accepted accounting terms. We've been through this before, but that's what you're doing.

Income is not equivalent to cash inflow. Assuming income is transacted with cash flow, income is a subset of cash inflow. Non-income cash inflow includes cash receipts for sales of assets not produced in the current period.

From a generally accepted accounting principles perspective, your paradigm confuses the income statement with the flow of funds statement. And the latter is a formal accounting statement used in all financial reporting suites.

And those generally accepted accounting principles are consistent from the micro bottom to the macro top (e.g. national income accounts and Fed flow of funds accounts)

You can do that, but it makes discussion with those who have some experience with/knowledge of real world financial accounting very difficult.

And I suspect that your resulting accounting paradigm will inevitably be internally inconsistent, which is very difficult to demonstrate holistically in a discussion like this becomes it becomes a constant frenzied cat chasing its tail thing.

Suppose I earn $100 in income. I choose to spend $40 on consumption. At that point, I have saved $60. No market is necessary for me to go and "buy" my savings. By not buying consumption I have saved and my wealth has increased by $60.

At the same time, I may sell $100 worth of IBM stock. Now, I have driven down the price of IBM even as I save.

On the other hand, suppose I earn $100 in income and spend $100. My savings is zero. Then I buy 100 shares of IBM (on margin). Now I have purchased capital, driving up its price, but I have not saved.

The capital markets serve to price capital. They don't have anything to do with clearing savings demands per se. Savings demands don't even show up in those markets.

Whatever the equilibrium price of IBM stock will be, it's not going to be a reflection of savings demands, but of the earning prospects of IBM as opposed to my borrowing rates and risk tolerance.

And one striking real world example of this is what Calculated Risk calls the "distressing gap". They note that generally speaking new housing starts move tightly with used home sales, except recently. Recently, the price of housing has plunged so much that it is not economical for housing suppliers to build new homes. Distressed owners, often banks -- are selling used houses at prices so low that homebuilders can't compete. So here is an example of a "housing market" -- our proxy for the capital market -- in which the prices are lousy for the purveyors of investment goods, even though demand for housing is strong enough to move a lot of units. The net result is little housing investment, although a lot of homes are being sold.

There is no investment good market, there is no savings market. There is just one big market for capital, and the price of capital in that market doesn't clear the demands for investment goods or the demands for savings. It clears so that households are indifferent between holding capital and holding bonds.

Well, what would you call the activity of clearing scrub from land? I would call it a "service". The important point is that the firm that sells the scrub-clearing services cannot build up an inventory of scrub-clearing while waiting for a farmer to come along and buy it. A firm that produces machines can build up an inventory of machines waiting for a factory to come along and buy them.

And if you really don't like scrub-clearing, what about software engineers who work at a firm programming all their computers? That's investment, and a service.

You can do that, but it makes discussion with those who have some experience with/knowledge of real world financial accounting very difficult."

But I *have* to throw away GAAP. Look at how GAAP handles inflation!!! Carleton's land is still down on the books at its 1948 purchase price! There is no way I could build a coherent economic model that conforms to GAAP.

Ganging up on Nick:
"your paradigm confuses the income statement with the flow of funds statement"

Yes -- exactly! Nick, you've made this point before: If you don't spend your money on X, you must spend it on Y -- but the argument here is that when I spend money on the purchase of capital, that need not be counted as income by anyone else in the economy (unless they were in the business of producing and selling capital). Hence the homebuilder example.

The other example of this distinction is the little circular economy I gave, in which everyone owes money to the person on their left, sells output to the person on their right, and buys output from the person on their left. In that case, if everyone decides to take 1/2 of their income and pay down some of their debts, then even though the same cash-flow is circulating, income drops by 1/2, because the repayment of debt does not appear on the income statement. It's not an income event even though everyone "does something" with all of their money (e.g. there is no hoarding of cash).

And come to think of it, this was the same point that Scott F. was making earlier. You have now 3 people ganging up on you about the distinction between cash-flow and income, as well as the distinction between income events and balance sheet events. I suspect Andy H. is on our side, too, but may be too polite to say it. :P

JKH: "My suggestion was not that economic theory must conform to accounting identities, but that economic analysis must conform to it, including all forecasting and risk analysis."

Nick Rowe: "Agreed. Certainly. (But if the forecast comes from a model that conforms to accounting identities, then the forecast will automatically conform to them too.)"

It seems to me that one major problem today is that policy makers in general seem ignorant of the necessity to conform to accounting identities. Instead, they make proposals that violate them or require unusual or unlikely conditions in order to meet them. (It is not always possible to make sense out of policy proposals, so we cannot be entirely sure of that. ;)) If economists of all stripes are cognizant of these identities, why does the economic profession en masse not speak up about such policy proposals?

First, you need to stop talking about the "flow of *funds*". What the heck are "funds"? You need to talk instead about the flow of *money* -- the medium of exchange. Because it is money that we buy and sell stuff with. If we talk about demand and supply, and buying and selling, in a monetary exchange economy, we are talking about the flow of money.

Second, of course the purchase and sale of newly-produced goods ("income") is just one of the things we do with money. And only in a very simple model like Paul Krugman's babysitting coop, where there is one good (babysitting services, that cannot be inventoried, I note) plus money is the flow of money identical to the flow of income. In a more complex model, where you add a second non-money non-newly-produced good, usually called "bonds", then there are two markets, and the flow of money in only one of those markets represents income.

But the simple babysitting model is still useful. It reveals some important truths that sometimes get missed in more complex models. And, empirically, the demand for money (I'm talking stock, of course) does seem to depend strongly on income. (Though I wouldn't preclude taking a broader view, and saying the demand for money depends on *all* transactions, not just income, as in the transactions approach MV=PT, as opposed to the simpler MV=PY.)

It might be useful to distinguish between those intermediate services that are capitalized as investments, and those final services that are produced as consumer goods/services.

Your example is that of a service that is capitalized as an investment. The same thing happens in the production of new housing, for example. But the final GDP calculation shows the value of the house or in your case the land improvement as an investment good. The service input is intermediate.

When I pick up my dry cleaning, the service is not capitalized. It is a final consumer good/service and part of the final GDP calculation.

The latter is the sense in which I would generally view services in the context of I = S, at the macro level, and for purposes of our discussion.

JKH: Can the firm that sells scrub-clearing services to farmers build up a stock of unsold inventory of land-clearing services? No. So that is an example of a newly-produced investment service where there are no inventories. So a sudden big increased demand by farmers to invest results in desired investment exceeding actual investment, even with no inventories to involuntarily decummulate. That was the point of my introducing that example.

The whole economy is moving towards a service economy. We have to get our heads around stopping thinking of the typical component of GDP being some physical manufactured widget, with widget-producers having unsold stocks of widgets waiting in boxes for buyers. It would be better to start thinking of an economy where most of GDP is produced to order. Haircuts are the simplest example. The haircut isn't produced until the customer walks in the door and places an order.

In my defense, things don't seem to work out very well if we let economists just talk about the economics while taking the accounting for granted. We end up with Eugene Fama insisting that a fiscal stimulus can't possibly be expansionary because the savings to finance it have to come from somewhere. It's true, sort of, in certain models, but the reasons for it are subtle. As a matter of accounting, it's blatantly false, although the reasons wouldn't necessarily be clear to someone without a knowledge of national income accounting. There is something to be said for forcing economists, when they're talking to a general audience, to do the accounting first before they do the economics. I'm not sure I approve of economists' just casually "doing it with models."

I believe Warren Mosler has written that the national debt = private savings. In what way is that incorrect?"

I'm going to take that one, even though it was addressed to Scott.

My guess is that Warren was either making special assumptions, or was speaking a little loosely (which is OK, because we all need to do that).

In a closed economy, with no investment, and where the government holds no assets, it would be true that the accumulated stock of the past flows of private saving (people sometimes use the word "savingS" to distinguish the stock from the flow) would equal the government debt.

If the government owns assets, then you have to distinguish gross from net debt, which I always find it hard to remember. If there's investment, you need to remember that some private savingS are held as capital. If it's an open economy, some private savingS are loans to foreigners (could be negative, of course).

Otherwise I think what you say Warren said is correct. (Unless I've missed something).

The whole economy is moving towards consumption being *delivered* and *sold* as services. But there are enormous supply chains with huge amounts of capital investment and multi-year lead times required before those services become available to be sold.

Microsoft spends 2 years developing a version of Office, then 1 year testing it (enterprise software is hard to test), and then makes it available as an "on-demand" download. That does not mean that we are in a haircut economy with the good being "produced" on-demand.

A friend of mine worked wrote specialized software for CT scanners. It was a small German start up that was later purchased by Siemens. They used to laugh about selling the same software to the U.S. for 10x what they charged European customers. Anyways, it takes about 1 year of development, and then *2* years of testing. The software is then loaded onto a workstation and a period of training occurs. And, of course a year or so is spent selling it to various customers.

Then you walk into your doctors office and get the "on-demand" CT scan. So service yes, but investment is even more important and the lead time between initial investment and realization of sale are much longer. It is just that in those intermediate steps, you do not see half completed widgets in a warehouse somewhere.

Andy: "We end up with Eugene Fama insisting that a fiscal stimulus can't possibly be expansionary because the savings to finance it have to come from somewhere."

Yep, that's an example of a (non-MMT) economist mistaking an accounting identity for an equilibrium condition.

My own views on this are peculiar, of course, because I say that it is only monetary exchange that makes Id=Sd false in any interesting way (i.e. false in a way that would cause recessions if Sd exceeds Id).

rsj: the way I think about what you are saying there (which I agree is important) is that when a firm invests, it does so based on its expectation of the flow of future demand for the future services that current investment will be able to produce. That's sort of what I had in mind in my upward-sloping IS curve posts.

"Yep, that's an example of a (non-MMT) economist mistaking an accounting identity for an equilibrium condition."

It depends on how you interpret it. Both Greg Mankiw and Scott Sumner interpret Fama to be talking (not very clearly) about an actual equilibrium condition. If that's the case, then the confusion is the result of his not being explicit about the accounting, which is still presumably being done correctly in the background.